Narrow Results

The quaternary alloy (QA) is simulated on the Bethe lattice (BL) in the form of AB_pC_qD_r and its phase diagrams are calculated by using the exact recursion relations (ERR) for the coordination number z = 3. The QA is designed on the BL by placing A atoms (spin-1/2) on the odd shells and randomly placing B (spin-3/2), C (spin-5/2) or D (spin-1) atoms with probabilities p, q and r, respectively, on the even shells. A compact form of formulation for the QA is obtained in the standard-random approach which can easily be reduced to ternary alloy (TA) and mixed-spin models by the appropriate values of the random variables p, q and r. The phase diagrams are calculated on the temperature and ratio of bilinear interaction parameter planes for given values of probabilities.

The mixed spin-1/2 and spin-1 Blume–Capel model is studied with randomly alternated coordination numbers (CN) on the Bethe lattice (BL) by utilizing the exact recursion relations. Two different CNs are randomly distributed on the BL by using the standard–random (SR) approach. It is observed that this model presents first-order phase transitions and tricritical points for variations of CNs 3 and 4, even if these behaviors are not displayed for the regular mixed-spin on the BL. The phase diagrams are mapped by obtaining the phase transition temperatures of the first- and second-order on several planes.

The A, B and C atoms with spin-1/2, spin-3/2 and spin-5/2 are joined together sequentially on the Bethe lattice in the form of ABCABC$\dots$ to simulate a molecule as a triple mixed-spin system. The spins are assumed to be interacting with only their nearest-neighbors via bilinear exchange interaction parameter in addition to crystal and external magnetic fields. The order-parameters are obtained in terms of exact recursion relations, then from the study of their thermal variations, the phase diagrams are calculated on the possible planes of our system. It is found that the model gives only second-order phase transitions in addition to the compensation temperatures.

The triangular-type Ising nanowire is constructed on the Bethe lattice (BL) by using the core-shell structure consisting of spin-3/2 atoms as the core and spin-1/2 atoms as the triangular shell. Each triangular plaquette of spins forms a nanoparticle which is connected to upper and lower plaquettes symmetrically. The additions of the plaquettes continue indefinitely until the thermodynamic limit to construct the nanowire. The inter- and intra-bilinear interaction parameters (J) are assumed to be positive or negative to simulate the ferromagnetic (FM) or antiferromagnetic (AFM) interactions, respectively. The crystal field for spin-3/2 and external magnetic field for all sites are also included into the model. After obtaining the formulation of the model in terms of exact recursion relations (ERRs), the thermal variations of magnetizations are studied in detail to obtain the phase diagrams. It is found that the model leads to different types of FM and AFM regions with various forms of phase transitions. It is also interesting that the model presents random or oscillatory magnetization behavior regions for the appropriate values of our system parameters.

The mixed spin-1/2 and spin-3/2 Blume–Capel (BC) model is considered on the Bethe lattice (BL) with randomly changing coordination numbers (CN) and examined in terms of exact recursion relations. A couple of two different CNs are changed randomly on the shells of the BL in terms of a standard–random approach to obtain the phase diagrams on possible planes of the system parameters. It is found from the thermal analysis of the order-parameters that the model only gives the second-order phase transitions as in the regular mixed case. As the probability of having larger CN increases, the temperatures of the critical lines also increase as expected.